To determine To decide: Whether the function f ( x ) = x 3 81 in the interval [ 0 , 3 ] is probability density function or not. Explanation Definition used: The function f is a probability density function of a random variable X in the interval [ a , b ] if 1. f ( x ) ≥ 0 for all x in the interval [ a , b ] . 2. ∫ a b f ( x ) d x = 1 . Calculation: Consider the given function f ( x ) = x 3 81 in the interval [ 0 , 3 ] . It is given that, the value of x is in the interval [ 0 , 3 ] . 0 ≤ x ≤ 3 0 3 ≤ x 3 ≤ 3 3 ( cube the values in the inequality ) 0 81 ≤ x 3 81 ≤ 27 81 ( divide by 81 ) 0 ≤ f ( x ) ≤ 108 ( ∵ f ( x ) = x 3 81 ) It is observed that, the condition 1 holds

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Chapter 11.1, Problem 6E

To determine

To decide: Whether the function f(x)=x381 in the interval [0,3] is probability density function or not.

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Chapter 11.1, Problem 5E

Chapter 11.1, Problem 7E

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